New rotation period measurements of 67,163 Kepler stars

The Kepler space telescope leaves a legacy of tens of thousands of stellar rotation period measurements. While many of these stars show strong periodicity, there exists an even bigger fraction of stars with irregular variability for which rotation periods are unknown. As a consequence, many stellar activity studies might be strongly biased toward the behavior of more active stars with measured rotation periods. To at least partially lift this bias, we apply a new method based on the Gradient of the Power Spectrum (GPS). The maximum of the gradient corresponds to the position of the inflection point (IP). It was shown previously that the stellar rotation period $P_{rot}$ is linked to the inflection point period $P_{IP}$ by the simple equation $P_{rot} = P_{IP}/\alpha$, where $\alpha$ is a calibration factor. The GPS method is superior to classical methods (such as auto-correlation functions (ACF)) because it does not require a repeatable variability pattern in the time series. From the initial sample of 142,168 stars with effective temperature $T_{eff}\leq6500K$ and surface gravity $log g\geq4.0$ in the Kepler archive, we could measure rotation periods for 67,163 stars by combining the GPS and the ACF method. We further report the first determination of a rotation period for 20,397 stars. The GPS periods show good agreement with previous period measurements using classical methods, where these are available. Furthermore, we show that the scaling factor $\alpha$ increases for very cool stars with effective temperatures below 4000K, which we interpret as spots located at higher latitudes. We conclude that new techniques (such as the GPS method) must be applied to detect rotation periods of stars with small and more irregular variabilities. Ignoring these stars will distort the overall picture of stellar activity and, in particular, solar-stellar comparison studies.